Rate selection for a quasi-orthogonal communication system

ABSTRACT

A selected rate is received for an apparatus based on a hypothesized signal-to-noise-and-interference ratio (SINR) for the apparatus, and characterized statistics of noise and interference observed at a receiver for the apparatus. Data are processed in accordance with the rate selected for the apparatus.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.11/150,417, filed Jun. 10, 2005, entitled RATE SELECTION FOR AQUASI-ORTHOGONAL COMMUNICATION SYSTEM, which application claims thebenefit of U.S. Provisional Patent Application Ser. No. 60/659,641,filed Mar. 7, 2005, entitled RATE PREDICTION WITH A MINIMUM MEAN SQUAREDERROR RECEIVER which is assigned hereof and hereby expresslyincorporated herein by reference.

BACKGROUND

I. Field

The present disclosure relates generally to data communication, and morespecifically to rate selection for a communication system.

II. Background

A wireless multiple-access communication system can concurrentlycommunicate with multiple terminals on the forward and reverse links.The forward link (or downlink) refers to the communication link from thebase stations to the terminals, and the reverse link (or uplink) refersto the communication link from the terminals to the base stations.Multiple terminals may simultaneously transmit data on the reverse linkand/or receive data on the forward link. This is often achieved bymultiplexing the transmissions on each link to be orthogonal to oneanother in time, frequency and/or code domain.

The terminals may be distributed throughout the system and mayexperience different channel conditions (e.g., different fading,multipath, and interference effects). Consequently, these terminals mayachieve different signal-to-noise-and-interference ratios (SNRs). TheSINR of a traffic channel determines its transmission capability, whichis typically quantified by a particular data rate that may be reliablytransmitted on the traffic channel. If the SINR varies from terminal toterminal, then the supported data rate would also vary from terminal toterminal. Moreover, since the channel conditions typically vary withtime, the supported data rates for the terminals would also vary withtime.

Rate control is a major challenge in a multiple-access communicationsystem. Rate control entails controlling the data rate of each terminalbased on the channel conditions for the terminal. The goal of ratecontrol should be to maximize the overall throughput while meetingcertain quality objectives, which may be quantified by a target packeterror rate (PER) and/or some other criterion.

There is therefore a need in the art for techniques to effectivelyperform rate control in a multiple-access communication system.

SUMMARY

Techniques for selecting a rate for a transmitter in a communicationsystem are described herein. A receiver obtains a channel responseestimate and a received SINR estimate for the transmitter, e.g., basedon a pilot received from the transmitter. The receiver computes ahypothesized SINR for the transmitter based on the channel responseestimate and the received SINR estimate. The receiver then selects arate for the transmitter based on the hypothesized SINR andcharacterized statistics of noise and interference at the receiver forthe transmitter.

The noise and interference for the transmitter is dependent on variousfactors such as the number of other transmitters causing interference tothis transmitter (which are called co-channel transmitters), the spatialprocessing technique used by the receiver to recover data transmissionssent by the transmitters, the number of antennas at the receiver, and soon. The characterized statistics of the noise and interference for thetransmitter may be given by a probability density function (PDF) of SINRloss with respect to the hypothesized SINR for the transmitter. Alook-up table of rate versus hypothesized SINR may be generated a priorifor the PDF of SINR loss. For each hypothesized SINR value, a capacitymay be computed based on the hypothesized SINR value, the PDF of SINRloss, and a capacity function. The computed capacity may be quantized toa rate supported by the system, and the rate and hypothesized SINR valuemay be stored in the look-up table. The receiver may then apply thehypothesized SINR for the transmitter to the look-up table, which wouldprovide the rate for the transmitter.

The rate selection techniques described herein are well suited for aquasi-orthogonal communication system in which (1) multiple transmitterscan transmit simultaneously on the same frequency subband in the sametime interval and (2) the exact noise and interference for thetransmitter are not known and only statistics of the noise andinterference are available. The exact noise and interference may not beknown because, e.g., the channel responses and the transmit powers ofthe co-channel transmitters are not known.

Various aspects and embodiments of the disclosure are described infurther detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

The features and nature of the present disclosure will become moreapparent from the detailed description set forth below when taken inconjunction with the drawings in which like reference charactersidentify correspondingly throughout.

FIG. 1 shows a communication system with multiple transmitters and areceiver according to an embodiment.

FIG. 2 shows a process for generating a look-up table of rate versushypothesized SINR according to an embodiment.

FIG. 3 shows a process for selecting a rate for a transmitter accordingto an embodument.

FIG. 4 shows a block diagram of two terminals and a base stationaccording to an embodument.

FIGS. 5A and 5B show plots of average unconstrained capacity and averageconstrained capacity, respectively, versus hypothesized SINR providedaccording to an embodument.

DETAILED DESCRIPTION

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any embodiment or design described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs.

FIG. 1 shows a wireless communication system 100 with multiple (M)transmitters 110 a through 110 m and a receiver 150, where M>1,according to an embodiment. For simplicity, each transmitter 110 isequipped with a single antenna 112, and receiver 150 is equipped withmultiple (R) antennas 152 a through 152 r, where R>1. For the forwardlink, each transmitter 110 may be part of a base station, and receiver150 may be part of a terminal. For the reverse link, each transmitter110 may be part of a terminal, and receiver 150 may be part of a basestation. FIG. 1 shows a time instant in which all M terminals 110 athrough 110 m concurrently transmit to receiver 150 on the samefrequency subband in the same time interval. In this case, R≧M.

A single-input multiple-output (SIMO) channel is formed between thesingle antenna at each transmitter and the R antennas at the receiver.The SIMO channel for transmitter m, for m=1, . . . , M, may becharacterized by an R×1 channel response vector h_(m), which may beexpressed as:

h_(m)=h_(m,1) h_(m,2) . . . h_(m,R)]^(T),   Eq (1)

where entry h_(m,j), for j=1, . . . , R, denotes the complex channelgain between the single antenna at transmitter m and antenna j at thereceiver, and “^(T)” denotes a transpose. A different SIMO channel isformed between each transmitter and the receiver. The channel responsevectors for the M transmitters may be denoted as h₁ through h_(M) andmay be assumed to be independent identically distributed (i.i.d.)complex Gaussian random vectors having the following properties:

h _(m) =N (0,R _(h))   Eq (2)

Equation (2) indicates that h_(m) has a normal Gaussian distribution, azero mean vector, and a covariance matrix of R_(h).

Each transmitter may transmit data and/or pilot from its single antennato the receiver. All M transmitters may transmit simultaneously viatheir respective SIMO channels to the receiver. The M transmitters maysend their transmissions on the same subband in the same time interval.In this case, each transmitter causes interference to the other M−1transmitters (which are called co-channel transmitters) and alsoobserves interference from the co-channel transmitters.

At the receiver, the received symbols for one subband in one symbolperiod may be expressed as:

r=H·s+n,   Eq (3)

where s is an M×1 vector with M data or pilot symbols sent by the Mtransmitters;

H=[h₁ h₂ . . . h_(m)] is an R×M channel response matrix;

n is an R×1 vector of noise and interference at the receiver; and

r is an R×1 vector with R received symbols from the R antennas at thereceiver.

As used herein, a data symbol is a modulation symbol for data, a pilotsymbol is a modulation symbol for pilot (which is a transmission that isknown a priori by both a transmitter and a receiver), and a modulationsymbol is a complex value for a point in a signal constellation (e.g.,for PSK, QAM, and so on). For simplicity, indices for subband and symbolperiod are not shown in equation (3) as well as the equations below.

In equation (3), H contains M columns, with each column correspondingto' a channel response vector for one transmitter. For simplicity, thenoise may be assumed to be additive white Gaussian noise (AWGN) with azero mean vector and a covariance matrix of σ_(o) ²·I, where σ_(o) ² isthe thermal noise plus inter-cell interference power (or total noise andinter-cell interference at the receiver) and I is the identity matrix.

The receiver may use various receiver spatial processing techniques toseparate out the overlapping transmissions sent by the M transmitters.These receiver spatial processing techniques include a minimum meansquare error (MMSE) technique, a zero-forcing (ZF) technique, and amaximal ratio combining (MRC) technique. The receiver may derive aspatial filter matrix based on the MMSE, ZF, or MRC technique, asfollows:

M _(mmse) =D _(mmse) ·[H ^(H) ·H+σ _(o) ² ·I] ⁻¹ ·H ^(H),   Eq (4)

M _(zf) =[H ^(H) ·H] ⁻¹ ·H ^(H),   Eq (5)

M _(mrc) =D _(mrc) ·H ^(H),   Eq (6)

where D_(mmse)=diag {M′_(mmse)·H}⁻¹ and M′_(mmse)=[H^(H)·H+σ_(o)²·I]⁻¹·H^(H);

D_(mrc)=diag [H^(H)·H]⁻¹; and

“^(H)” denotes a conjugate transpose.

D_(mmse) and D_(mrc) are diagonal matrices of scaling values used toobtain normalized estimates of the transmitted data symbols. Thereceiver may obtain an estimate of H based on pilots received from the Mtransmitters. For simplicity, the description herein assumes no channelestimation error.

The receiver may perform receiver spatial processing as follows:

ŝ=M·r=s+ñ,   Eq (7)

where M is a spatial filter matrix, which may be equal to M_(mmse),M_(zf) or M_(mrc);

ŝ is an M×1 vector with M data symbol estimates; and

ñ is a vector of noise and interference after the receiver spatialprocessing.

The data symbol estimates in ŝ are estimates of the transmitted datasymbols in s.

For the MMSE technique, the post-detection SINR for each transmitter m,which is the SINR after the receiver spatial processing, may beexpressed as:

SINR_(mmse,m) =P _(m) ·h _(m) ^(H) ·R _(mmse,m) ⁻¹ ·h _(m),   Eq (8)

where P_(m) is the transmit power for transmitter m; and

R_(mmse,m) is an M×M covariance matrix applicable to transmitter m.

The transmit power for transmitter m may be given as:

P _(m) =P _(ref) +ΔP _(m),   Eq (9)

where P_(ref) is a reference power level and ΔP_(m) is a transmit powerdelta. The reference power level is the amount of transmit power neededto achieve a target SINR for a designated transmission, which may besignaling sent by transmitter m on a control channel. The referencepower level and the target SINR may be adjusted via one or more powercontrol loops to achieve a desired level of performance for thedesignated transmission, e.g., 1% PER. The target SINR may be dependenton a rise-power-over-thermal (RpOT) operating point selected for thesystem. ΔP_(m) may be adjusted via another power control loop tomaintain inter-cell interference within acceptable levels. The transmitpower P_(m) may also be determined in other manners besides equation(9).

The covariance matrix R_(mmse,m) may be expressed as:

$\begin{matrix}{{\underset{\_}{R}}_{{mmse},m} = {{\sum\limits_{{q = 1},{q \neq m}}^{M}{P_{q} \cdot {\underset{\_}{h}}_{q} \cdot {\underset{\_}{h}}_{q}^{H}}} + {\sigma_{o}^{2} \cdot {\underset{\_}{I}.}}}} & {{Eq}\mspace{14mu} (10)}\end{matrix}$

R_(mmse,m) is indicative of the total noise and interference observed atthe receiver for transmitter m. This total noise and interferenceincludes (1) intra-cell interference from the co-channel transmitters,which is given by the summation of P_(q)·h_(q)·h_(q) ^(H) for q=1, . . ., M and q≠m, and (2) thermal noise and inter-cell interference, which isgiven by the term σ_(o) ²·I.

The ergodic unconstrained capacity for transmitter m, C_(m), may beexpressed as:

C _(m)=log₂ [1+SINR_(m)],   Eq (11)

where SINR_(m) is the SINR of transmitter m. The ergodic unconstrainedcapacity is the theoretical capacity of a communication channel andindicates the maximum data rate that may be reliably transmitted via thecommunication channel. If the ergodic unconstrained capacity is knownfor transmitter m, then a suitable rate may be selected for transmitterm such that data is transmitted at or near the capacity of thecommunication channel for transmitter m.

The ergodic unconstrained capacity is dependent on the SINR oftransmitter m, which for the MMSE technique is dependent on thecovariance matrix R_(mmse,m), as shown in equation (8). R_(mmse,m) is inturn dependent on the channel response vectors and the transmit powersfor the co-channel transmitters, which may be unknown at the time a rateis to be selected for transmitter m. For example, the system may employfrequency hopping so that each transmitter hops from subband to subbandin different time intervals in order to achieve frequency diversity. Inthis case, transmitter m observes interference from different sets ofco-channel transmitters in different time intervals. As another example,transmitter m may have just accessed the system, and the channelresponse vectors and the transmit powers for the co-channel transmittersmay not be known.

Although the channel response vectors, h, for q=1, . . . , M and q≠m,and the transmit powers, P_(q) for q=1, . . . , M and q≠m, for theco-channel transmitters may not be known, statistics such as thedistribution of the transmit powers and the distribution of the channelresponse vectors for the co-channel transmitters may be known.Furthermore, the total noise and inter-cell interference σ_(o) ² at thereceiver may also be known. An expected or average ergodic unconstrainedcapacity for transmitter m for the MMSE technique may then be expressedas:

C _(mmse,m) =E

log ₂[1+SINR_(mmse,m)(R _(mmse,m))]

,   Eq (12)

where E( ) is an expectation operation. Equation (12) assumes that thechannel response vector h_(m) and the transmit power P_(m) for thedesired transmitter m are known. Hence, the expectation operation inequation (12) is taken over only the distribution of R_(mmse,m) (and notover h_(m) and P_(m), which are assumed to be known). The evaluation ofequation (12) may be simplified as described below.

The post-detection SINR in equation (8) may be expressed as:

SINR_(mmse,m) =P _(m) ·|h _(m)|² ·u _(m) ^(H) ·R _(mmse,m) ⁻¹ ·u _(m),  Eq (13)

where u_(m)=h_(m)/|h_(m)| is a normalized channel response vector fortransmitter m. u_(m) is a unit norm vector obtained by dividing eachelement of h_(m) by the norm of h_(m). An orthonormal matrix U may bedefined such that u_(m) is the m-th column of U. The orthonormal matrixU has the following properties:

U·U ^(H) =U ^(H) ·U=I and U ⁻¹ =U ^(H)   Eq (14)

Equation set (14) indicates that the M rows of the orthonormal matrix Uare orthogonal to one another, the M columns of U are also orthogonal toone another, and each column of U has unit power.

Two matrices X and Y may be defined as follows:

X=U ^(H) ·R _(mmse,m) ⁻¹ ·U, and   Eq (15)

Y=R _(mmse,m) ⁻¹.   Eq (16)

It can be shown that matrices X and Y are identically distributed andthat their elements are also identically distributed. To see this,matrix X may be rewritten as follows:

$\begin{matrix}\begin{matrix}{\underset{\_}{X} = {{\underset{\_}{U}}^{H} \cdot {\underset{\_}{R}}_{{mmse},m}^{- 1} \cdot \underset{\_}{U}}} \\{= \left\lbrack {{\underset{\_}{U}}^{- 1} \cdot R_{{mmse},m} \cdot \left( {\underset{\_}{U}}^{H} \right)^{- 1}} \right\rbrack^{- 1}} \\{{= \left\lbrack {{\underset{\_}{U}}^{H} \cdot {\underset{\_}{R}}_{{mmse},m} \cdot \underset{\_}{U}} \right\rbrack^{- 1}},} \\{{= \left( {{\sum\limits_{{q = 1},{q \neq m}}^{M}{P_{q} \cdot {\underset{\_}{U}}^{H} \cdot {\underset{\_}{h}}_{q} \cdot {\underset{\_}{h}}_{q}^{H} \cdot \underset{\_}{U}}} + {\sigma_{o}^{2} \cdot \underset{\_}{I} \cdot {\underset{\_}{U}}^{H} \cdot \underset{\_}{U}}} \right)^{- 1}},} \\{{= \left( {{\sum\limits_{{q = 1},{q \neq m}}^{M}{P_{q} \cdot {\underset{\_}{v}}_{q} \cdot {\underset{\_}{v}}_{q}^{H}}} + {\sigma_{o}^{2} \cdot \underset{\_}{I}}} \right)^{- 1}},}\end{matrix} & {{Eq}\mspace{11mu} (17)}\end{matrix}$

where v_(q)=U^(H)·h_(q). It can be shown that v_(q) for q=1, . . . , Mare i.i.d. complex Gaussian random Vectors and are distributed asN(0,R_(h)).

Matrix Y may be rewritten as follows:

$\begin{matrix}{\underset{\_}{Y} = {\left( {{\sum\limits_{{q = 1},{q \neq m}}^{M}{P_{q} \cdot {\underset{\_}{h}}_{q} \cdot {\underset{\_}{h}}_{q}^{H}}} + {\sigma_{o}^{2} \cdot \underset{\_}{I}}} \right)^{- 1}.}} & {{Eq}\mspace{14mu} (18)}\end{matrix}$

Comparing equations (17) and (18), it can be seen that X and Y areidentically distributed. Furthermore, the elements of X and Y are alsoidentically distributed.

A random variable X_(m) for row m and column m of X may be expressed as:

X _(m) =u _(m) ^(H) ·R _(mmse,m) ⁻¹ ·u _(m).   Eq (19)

Equation (19) indicates that the exact value of X_(m) is dependent onboth (1) the normalized channel response vector u_(m) for transmitter mand (2) the channel response vectors for the co-channel transmitters,which are included in R_(mmse,m) ⁻¹. However, because the elements of Xand Y are identically distributed, the random variable X_(m) isidentically distributed as a random variable Y_(m) for row m and columnm of Y. Since Y is only dependent on the channel response vectors forthe co-channel transmitters, the random variable X_(m) is also dependentonly on the co-channel transmitters.

The post-detection SINR of transmitter m in equation (13) may beexpressed as:

SINR_(mmse,m) =P _(m) ·|h _(m)|² ·u _(m) ^(H) ·R _(mmse,m) ⁻¹ ·u _(m) =S_(m) ·L _(mmse),   Eq (20)

where

$\begin{matrix}{{S_{m} = {\frac{P_{m}}{\sigma_{o}^{2}} \cdot {{\underset{\_}{h}}_{m}}^{2}}},} & {{Eq}\mspace{14mu} (21)} \\{{L_{mmse} = {{\underset{\_}{u}}_{m}^{H} \cdot \sigma_{o}^{2} \cdot {\underset{\_}{R}}_{{mmse},m}^{- 1} \cdot {\underset{\_}{u}}_{m}}},{and}} & {{Eq}\mspace{14mu} (22)} \\{{\sigma_{o}^{2} \cdot {\underset{\_}{R}}_{{mmse},m}^{- 1}} = {\left( {{\sum\limits_{{q = 1},{q \neq m}}^{M}{\frac{P_{q}}{\sigma_{o}^{2}} \cdot {\underset{\_}{h}}_{q} \cdot {\underset{\_}{h}}_{q}^{H}}} + \underset{\_}{I}} \right)^{- 1}.}} & {{Eq}\mspace{14mu} (23)}\end{matrix}$

In equations (20) through (23), S_(m) represents a hypothesized SINR fortransmitter m after the receiver spatial processing if there is nointerference from other transmitters. S_(m) is dependent on the receivedSINR P_(m)/σ_(o) ² and the channel norm |h_(m)|² for transmitter m.L_(mmse) represents the SINR loss with respect to the hypothesized SINRdue to the presence of interference from the co-channel transmitterswith the MMSE technique.

For the zero-forcing technique, the post-detection SINR for eachtransmitter m may be expressed as:

$\begin{matrix}{{{SINR}_{{zf},m} = \frac{P_{m}}{R_{{zf},m}}},} & {{Eq}\mspace{14mu} (24)}\end{matrix}$

where R_(zf,m) is the first diagonal element of an M×M covariance matrixR_(zf,m) for the zero-forcing technique. R_(zf,m) may be expressed as:

R _(zf,m)=σ_(o) ²·(H _(m) ^(H) ·H _(m))⁻¹.   Eq (25)

where H_(m) is a re-ordered version of H and contains h_(m) in the firstcolumn.

Matrix (H_(m) ^(H)·H_(m))⁻¹ may be expressed as:

$\begin{matrix}{{\left( {{\underset{\_}{H}}_{m}^{H} \cdot {\underset{\_}{H}}_{m}} \right)^{- 1} = \begin{bmatrix}{{\underset{\_}{h}}_{m}^{H} \cdot {\underset{\_}{h}}_{m}} & {{\underset{\_}{h}}_{m}^{H} \cdot \underset{\_}{A}} \\{\underset{\_}{A} \cdot {\underset{\_}{h}}_{m}} & {{\underset{\_}{A}}^{H} \cdot \underset{\_}{A}}\end{bmatrix}^{- 1}},} & {{Eq}\mspace{14mu} (26)}\end{matrix}$

where A=[h₁ . . . h_(m−1) h_(m+1) . . . h_(M)] is an R×(M−1) matrixcontaining all columns of H except for h_(m). R_(zf,m) is the (1,1)element of σ_(o) ²·(H_(m) ^(H)·H_(m))⁻¹ and may be expressed as:

$\begin{matrix}\begin{matrix}{{R_{{zf},m} = {\sigma_{o}^{2} \cdot \left\lbrack {{{\underset{\_}{h}}_{m}^{H} \cdot {\underset{\_}{h}}_{m}} - {{\underset{\_}{h}}_{m}^{H} \cdot \underset{\_}{A} \cdot \left( {{\underset{\_}{A}}^{H} \cdot \underset{\_}{A}} \right)^{- 1} \cdot {\underset{\_}{A}}^{H} \cdot {\underset{\_}{h}}_{m}}} \right\rbrack^{- 1}}},} \\{{= {\sigma_{o}^{2} \cdot \left\lbrack {{{\underset{\_}{h}}_{m}}^{2} \cdot \left( {1 - {{\underset{\_}{u}}_{m}^{H} \cdot \underset{\_}{A} \cdot \left( {{\underset{\_}{A}}^{H} \cdot \underset{\_}{A}} \right)^{- 1} \cdot {\underset{\_}{A}}^{H} \cdot {\underset{\_}{u}}_{m}}} \right)} \right\rbrack^{- 1}}},} \\{{= {\sigma_{o}^{2} \cdot \left\lbrack {{{\underset{\_}{h}}_{m}}^{2} \cdot \left( {1 - Z_{m}} \right)} \right\rbrack^{- 1}}},}\end{matrix} & {{Eq}\mspace{11mu} (27)}\end{matrix}$

where u_(m)=h_(m)/|h_(m)| and Z_(m)=u_(m)^(H)·A·(A^(H)·A)⁻¹·A^(H)·u_(m).

An orthonormal matrix U may be defined such that u_(m) is the firstcolumn of U. A matrix V may be defined as:

$\begin{matrix}\begin{matrix}{{\underset{\_}{V} = {{\underset{\_}{U}}^{H} \cdot \underset{\_}{A} \cdot \left( {{\underset{\_}{A}}^{H} \cdot \underset{\_}{A}} \right)^{- 1} \cdot {\underset{\_}{A}}^{H} \cdot \underset{\_}{U}}},} \\{{= {{\underset{\_}{U}}^{H} \cdot \underset{\_}{A} \cdot \left( {{\underset{\_}{A}}^{H} \cdot \underset{\_}{U} \cdot {\underset{\_}{U}}^{H} \cdot \underset{\_}{A}} \right)^{- 1} \cdot {\underset{\_}{A}}^{H} \cdot \underset{\_}{U}}},} \\{{= {\underset{\_}{B} \cdot \left( {{\underset{\_}{B}}^{H} \cdot \underset{\_}{B}} \right)^{- 1} \cdot {\underset{\_}{B}}^{H}}},}\end{matrix} & {{Eq}\mspace{14mu} (28)}\end{matrix}$

where B=U^(H)·A. As indicated by equation (28),U^(H)·A·(A^(H)·A)⁻¹·A^(H)·U has the same distribution asB·(B^(H)·B)⁻¹·B^(H), which has the same distribution asA·(A^(H)·A)⁻¹·A^(H). This results from (1) the columns of A being i.i.d.complex Gaussian random vectors and distributed as N(0,R_(h)) and (2)the multiplications with U^(H) and U being unitary transformations.Hence, random variable Z_(m) for u_(m) ^(H)·A·(A^(H)·A)⁻¹·A^(H)·u_(m) isdistributed as the (1, 1) element of B·(B^(H)·B)⁻¹·B^(H).

The post-detection SINR in equation (24) for the zero-forcing techniquemay then be expressed as:

$\begin{matrix}{{{SINR}_{{zf},m} = {{\frac{P_{m}}{\sigma_{o}^{2}} \cdot {{\underset{\_}{h}}_{m}}^{2} \cdot \left( {1 - Z_{m}} \right)} = {{S_{m} \cdot \left( {1 - Z_{m}} \right)} = {S_{m} \cdot L_{zf}}}}},} & {{Eq}\mspace{14mu} (29)}\end{matrix}$

where

$S_{m} = {\frac{P_{m}}{\sigma_{o}^{2}} \cdot {{\underset{\_}{h}}_{m}}^{2}}$

and L_(zf)=1−Z_(m). S_(m) represents the hypothesized SINR fortransmitter m with no interference from other transmitters. L_(zf)represents the SINR loss due to the presence of interference from theco-channel transmitters with the zero-forcing technique.

For the MRC technique, the post-detection SINR for each transmitter mmay be expressed as:

$\begin{matrix}{{{SINR}_{{mrc},m} = {\frac{P_{m} \cdot \left( {{\underset{\_}{h}}_{m}}^{2} \right)^{2}}{{\underset{\_}{h}}_{m}^{H} \cdot R_{{mrc},m} \cdot {\underset{\_}{h}}_{m}} = \frac{P_{m} \cdot {{\underset{\_}{h}}_{m}}^{2}}{{\underset{\_}{u}}_{m}^{H} \cdot {\underset{\_}{R}}_{{mrc},m} \cdot {\underset{\_}{u}}_{m}}}},} & {{Eq}\mspace{14mu} (30)}\end{matrix}$

where u_(m)=h_(m)/|h_(m)| and

$\begin{matrix}{{\underset{\_}{R}}_{{mrc},m} = {{\sum\limits_{{q = 1},{q \neq m}}^{M}{P_{q} \cdot {\underset{\_}{h}}_{q} \cdot {\underset{\_}{h}}_{q}^{H}}} + {\sigma_{o}^{2} \cdot {\underset{\_}{I}.}}}} & {{Eq}\mspace{14mu} (31)}\end{matrix}$

A matrix C may be defined as:

C=U ^(H) ·R _(mrc,m) ·U,   Eq (32)

where U is an orthonormal matrix containing u_(m), as the m-th column.

A random variable M_(m) for the (n, m) element of C may be expressed as:

M _(m) =u _(m) ^(H) ·R _(mrc,m).   Eq (33)

It can be shown that random variable M_(m) is distributed as the (m, m)element of R_(mrc,m).

The post-detection SINR in equation (30) for the MRC technique may thenbe expressed as:

$\begin{matrix}{{{SINR}_{{mrc},m} = {\frac{P_{m} \cdot {{\underset{\_}{h}}_{m}}^{2}}{\sigma_{o}^{2} \cdot \left( {M_{m}/\sigma_{o}^{2}} \right)} = {S_{m} \cdot L_{mrc}}}},} & {{Eq}\mspace{14mu} (34)}\end{matrix}$

where

$S_{m} = {\frac{P_{m}}{\sigma_{o}^{2}} \cdot {{\underset{\_}{h}}_{m}}^{2}}$

and L_(mrc)=σ_(o) ²/M_(m). L_(mrc) represents the SINR loss due to thepresence of interference from the co-channel transmitters with the MRCtechnique.

In general, the post-detection SINR for each terminal m may be expressedas:

SINR_(m) =S _(m) ·L _(m),   Eq (35)

where L_(m) is the SINR loss due to interference from the co-channeltransmitters and may be equal to L_(mmse), L_(zf) or L_(mrc). Theaverage ergodic unconstrained capacity may be expressed as:

$\begin{matrix}{{C_{m} = {\int_{x}{{\log_{2}\left\lbrack {1 + {S_{m} \cdot L_{m}}} \right\rbrack} \cdot {f_{L}(x)} \cdot \ {x}}}},} & {{Eq}\mspace{14mu} (36)}\end{matrix}$

where ƒ_(L)(x) is a probability density function (PDF) of the randomvariable L_(m). The function ƒ_(L)(x) is dependent on the receiverspatial processing technique selected for use, e.g., MMSE, zero-forcing,or MRC. The expectation operation over SINR_(m) in equation (12) isreplaced by an integration over ƒ_(L)(x) in equation (36). ƒ_(L)(x) maybe determined analytically by using the properties of the complexWishart distribution of complex random matrices. ƒ_(L)(x) may also bedetermined via computer simulations (e.g., Monte Carlo simulations), byempirical measurements in the field, or by some other means.

Equation (36) provides an average unconstrained capacity of acommunication channel for a transmitter. A constrained capacity of thecommunication channel is further dependent on a specific modulationscheme used for data transmission. The constrained spectral efficiency(due to the fact that the modulation symbols are restricted to specificpoints on a signal constellation) is lower than the unconstrainedcapacity (which is not confined by any signal constellation).

The constrained capacity for transmitter m may be expressed as:

$\begin{matrix}{C_{m} = {B - {\quad{\frac{1}{2^{B}}{\sum\limits_{i = 1}^{2^{B}}{E{\quad{\left( {\log_{2}{\sum\limits_{j = 1}^{2^{B}}{\exp\left( {{- {SINR}_{m}} \cdot \begin{pmatrix}{{{a_{i} - a_{j}}}^{2} +} \\{2\; {Re}\left\{ {\beta^{*}\left( {a_{i} - a_{j}} \right)} \right\}}\end{pmatrix}} \right)}}} \right),}}}}}}}} & {{Eq}\mspace{14mu} (37)}\end{matrix}$

where B is the number of bits for each signal point in a 2^(B)-arysignal constellation;

-   -   a_(i) and a_(j) are signal points in the 2^(B)-ary signal        constellation; and    -   β is a complex Gaussian random variable with zero mean and        variance of 1/SINR_(m).        The 2^(B)-ary signal constellation contains 2^(B) signal points        for a specific modulation scheme, e.g., QPSK, 16-QAM, and so on.        Each signal point is a complex value that may be used for a        modulation symbol. The expectation operation in equation (37) is        taken with respect to the random variable β. The constrained        capacity in equation (37) is a function of the signal points in        the constellation as well as SINR_(m).

The average constrained capacity for transmitter m may be expressed as:

$\begin{matrix}{C_{m} = {\int_{x}\; {\begin{pmatrix}{B - {\frac{1}{2^{B}} {\sum\limits_{i = 1}^{2^{B}}E}}} \\{\quad\left( {\log_{2}{\sum\limits_{j = 1}^{2^{B}}{\exp \left( {{- S_{m}} \cdot L_{m} \cdot \begin{pmatrix}{{{a_{i} - a_{j}}}^{2} +} \\{2\; {Re}\left\{ {\beta^{*}\left( {a_{i} - a_{j}} \right)} \right\}}\end{pmatrix}} \right)}}}\  \right)}\end{pmatrix} \cdot {f_{L}(x)} \cdot {{x}.}}}} & {{Eq}\mspace{14mu} (38)}\end{matrix}$

In equation (38), SINR_(m) is substituted with S_(m)·L_(m), and anintegration is performed over the probability density function of SINRloss L_(m). Equations (36) and (38) indicate that, for a given PDFfunction ƒ_(L)(x), the average capacity and hence the rate fortransmitter m may be predicted based on an estimated channel norm|h_(m)|² and an estimated received SINR P_(m)/σ_(o) ² for transmitter m.

While the above discussion, discusses an embodiment of a SIMO systemformed between a single antenna at a transmitter and R antennas at thereceiver, the above approach may also be applied to a multi-inputmulti-output (MIMO) system formed between multiple antennas at atransmitter and R antennas at the receiver. In an embodiment, this maybe provided by treating each transmission stream from each antenna atthe transmitter as a separate transmitter. In this embodiment, the othertransmissions from other antennas at the same transmitter are considerednoise. As such in the case where equation 3 is utilized thetransmissions from the other antennas may be used in calculating n. Therate may then be determined as otherwise discussed above, with theprovision that the rate determined may be thought of as a floor

FIG. 2 shows a process 200 for generating a look-up table of rate versushypothesized SINR for a given PDF function ƒ_(t)(x) of SINR lossaccording to an embodiment. The function ƒ_(L)(x) is initiallydetermined, e.g., by analytical computation, via computer simulations,based on actual measurements for transmitters in the system, based on anassumption of the worst case channel conditions for the transmitters, orin some other manner (block 212). A value of S_(m) is selected (block214). A capacity C_(m) is computed based on the selected value of S_(m),the PDF function ƒ_(L)(x), and a capacity function such as equation (36)or (38) (block 216). A rate R_(m) is determined for the selected valueof S_(m) based on the computed capacity C_(m) (block 218). The rateR_(m) and the selected value of S_(m) are stored in the look-up table(block 220). If another value of S_(m) is to be evaluated, as determinedin block 222, then the process returns to block 214. Otherwise, theprocess terminates.

The system may support a set of rates. Table 1 lists an exemplary set of14 rates supported by the system, which are given indices of 0 through13. Each supported rate may be associated with a specific data rate orspectral efficiency, a specific modulation scheme, and a specific coderate. Spectral efficiency may be given in units of bits/second/Hertz(bps/Hz).

TABLE 1 Rate Spectral Code Modulation Index Efficiency Rate Scheme 0 0.0— — 1 0.25 1/4 BPSK 2 0.5 1/2 BPSK 3 1.0 1/2 QPSK 4 1.5 3/4 QPSK 5 2.01/2 16 QAM 6 2.5 5/8 16 QAM 7 3.0 3/4 16 QAM 8 3.5  7/12 64 QAM 9 4.02/3 64 QAM 10 4.5 3/4 64 QAM 11 5.0 5/6 64 QAM 12 6.0 3/4 256 QAM  137.0 7/8 256 QAM 

In an embodiment, for block 218 in FIG. 2, the capacity C_(m) for eachvalue of S_(m) is compared against the spectral efficiencies for thesupported rates, and the supported rate with the highest spectralefficiency that is less than or equal to the capacity C_(m) is selectedfor that value of S_(m). The capacity C_(m) is effectively quantized tothe nearest (lower) rate supported by the system. In another embodiment,a back-off factor is applied to the capacity C_(m) (e.g.,C_(bo,m)=C_(m)·K_(bo), where K_(bo)<1), and the backed-off capacityC_(bo,m) is compared against the spectral efficiencies for the supportedrates to determine the rate for the value of S_(m). The back-off factormay be used to account for rate prediction errors, which may be due tomischaracterization of the SINR loss, use of an unconstrained capacityfunction to simplify computation, and so on. The back-off factor mayalso be accounted for in the computation of S_(m), in the PDF functionƒ_(L)(x), in the computation of C_(m), and so on.

Table 2 shows an exemplary look-up table generated for a specificoperating scenario in an exemplary system. For this operating scenario,the receiver is equipped with four antennas (R=4) and there are twoco-channel transmitters (M=2). Table 2 shows the average unconstrainedcapacity (in bps/Hz) and the rate (also in bps/Hz) for different valuesof S_(m) (in dB).

TABLE 2 Hypothesized Capacity Rate SINR S_(m) C_(m) R_(m) 0.0 0.9 0.51.0 1.0 1.0 2.0 1.2 1.0 3.0 1.4 1.0 4.0 1.6 1.5 5.0 1.8 1.5 6.0 2.1 2.07.0 2.3 2.0 8.0 2.6 2.5 9.0 2.9 2.5 10.0 3.2 3.0

In general, the noise and interference for transmitter m is dependent onvarious factors such as, for example, (1) the number of co-channeltransmitters, which is typically known for the system, (2) the receiverspatial processing technique used by the receiver, which is also knownand affects the distribution of L_(m), (3) the number of antennas at thereceiver, (4) the distribution of channel response vectors and thedistribution of transmit powers for the co-channel transmitters, and (5)possibly other factors. The noise and interference for transmitter m maynot be known exactly if the channel responses and transmit powers forthe co-channel transmitters are not known. However, characterizedstatistics of the noise and interference for transmitter m may be knownand may be given in various formats such as, for example, (1) aprobability density function of SINR loss L_(m), as described above, (2)a mean, a standard deviation, and a specific distribution of SINR lossL_(m) (e.g., a Gaussian distribution that is representative of theworst-case distribution of L_(m)), or (3) some other formats and/orstatistics.

FIG. 2 shows the generation of a look-up table of rate versushypothesized SINR for a specific noise and interference characterizationor operating scenario. Process 200 may be performed for different noiseand interference characterizations to obtain a look-up table of rateversus hypothesized SINR for each noise and interferencecharacterization. For example, process 200 may be performed for eachpossible value of M (e.g., for M=1, 2, 3 and so on) to obtain a look-uptable for each value of M. M determines the number of co-channeltransmitters and hence affects the interference observed by transmitterm from the co-channel transmitters. Process 200 may also be performedfor each possible receiver spatial processing technique (e.g., MMSE,zero-forcing, and MRC) to obtain a look-up table for each receiverspatial processing technique. Different receiver processing techniqueshave different noise and interference characteristics that affect thecapacity and hence the rate for a transmitter.

FIG. 5A shows plots of the average unconstrained capacity C_(m) versushypothesized SINR S_(m) for the exemplary system described above withfour antennas at the receiver and using the MMSE technique. Plots 510,512, and 514 show the average unconstrained capacity versus hypothesizedSINR for M=1, M=2, and M=3, respectively.

FIG. 5B shows plots of the average constrained capacity C_(m) versushypothesized SINR S_(m) for 16-QAM in the exemplary system noted abovewith the MMSE technique. Plots 520, 522, and 524 show the averageconstrained capacity versus hypothesized SINR for M=1, M=2, and M=3,respectively.

FIG. 3 shows a process 300 for selecting a rate for transmitter m.Initially, a channel response vector h_(m) and a received SINRP_(m)/σ_(o) ² are estimated for transmitter m, e.g., based on a pilotreceived from transmitter m (block 312), according to an embodiment. Ahypothesized SINR S_(m) is then computed for transmitter m based on thechannel response vector and the received SINR, as shown in equation (21)(block 314). Characterized statistics of the noise and interference fortransmitter m are determined (block 316). A suitable rate R_(m) is thenselected for transmitter m based on the hypothesized SINR S_(m) and thecharacterized statistics of the noise and interference for transmitter m(block 318).

Blocks 316 and 318 in FIG. 3 may be performed implicitly. A differentlook-up table of rate versus hypothesized SINR may be generated for eachdifferent noise and interference characterization. For example, alook-up table may be generated for M=2 and R=3, another look-up tablemay be generated for M=3 and R=4, and so on. Each look-up table isgenerated based on the characterized statistics of the noise andinterference (e.g., a probability density function of SINR loss L_(m))applicable for that operating scenario. The rate R_(m) for transmitter mmay then be obtained by applying the computed hypothesized SINR S_(m) tothe look-up table for the noise and interference characterizationapplicable to transmitter m.

The computation of capacity based on hypothesized SINR and characterizedstatistics of noise and interference and the mapping of capacity to ratemay be performed a priori and stored in one or more look-up tables, asdescribed above in FIG. 2. Alternatively, the noise and interferencestatistics may be updated based on field measurements, and the capacitycomputation may be performed in realtime based on the updated statisticsof the noise and interference.

For simplicity, the description above assumes that each transmitter isequipped with a single antenna. In general, any number of transmittersmay transmit simultaneously to the receiver, and each transmitter may beequipped with any number of antennas, subject to the condition that upto R data streams may be sent simultaneously to the R antennas at thereceiver. If one data stream is sent from each transmitter antenna, thenM≦R. A transmitter may transmit multiple data streams from multipleantennas, in which case the channel response matrix H would include onecolumn for each transmitter antenna. A transmitter may also transmit onedata stream from multiple antennas (e.g., using beamforming), in whichcase the channel response matrix H would include one column for aneffective communication channel observed by the data stream.

FIG. 4 shows a block diagram of two terminals 410 x and 410 y and a basestation 450 in a communication system 400 according to an embodiment. Onthe reverse link, at each terminal 410, a transmit (TX) data processor412 encodes, interleaves, and symbol maps traffic and control data andprovides data symbols. A modulator (Mod) 414 maps the data symbols andpilot symbols onto the proper subbands and symbol periods, performs OFDMmodulation if applicable, and provides a sequence of complex-valuedchips. The pilot symbols are used by base station 450 for channelestimation. A transmitter unit (TMTR) 416 conditions (e.g., converts toanalog, amplifies, filters, and frequency upconverts) the sequence ofchips and generates a reverse link signal, which is transmitted via anantenna 418.

At base station 450, multiple antennas 452 a through 452 r receive thereverse link signals from terminals 410. Each antenna 452 provides areceived signal to a respective receiver unit (RCVR) 454. Each receiverunit 454 conditions (e.g., filters, amplifies, frequency downconverts,and digitizes) its received signal, performs OFDM demodulation ifapplicable, and provides received symbols. A receive (RX) spatialprocessor 460 performs receiver spatial processing on the receivedsymbols from all receiver units 454 and provides data symbol estimates.An RX data processor 462 demaps, deinterleaves, and decodes the datasymbol estimates and provides decoded data for the terminals.

The processing for forward link transmissions may be performed similarlyto that described above for the reverse link. The processing for thetransmissions on the forward and reverse links is typically specified bythe system.

For rate control, at base station 450, RX spatial processor 460 deriveschannel estimates (e.g., a channel response estimate h_(m) and areceived SINR estimate P_(m)/σ_(o) ²) for each terminal and provides thechannel estimates to a controller 470. Controller 470 computes ahypothesized SINR for each terminal based on the channel responseestimate and the received SINR estimate for that terminal. Controller470 then determines a rate for each terminal based on the hypothesizedSINR and using, e.g., a look-up table generated by process 200 in FIG.2. The rates for all terminals are processed by a TX data processor 482and a TX spatial processor 484, conditioned by transmitter units 454 athrough 454 r, and transmitted via antennas 452 a through 452 r.

At each terminal 410, antenna 418 receives the forward link signals frombase station 450 and provides a received signal to a receiver unit 416.The received signal is conditioned and digitized by receiver unit 416and further processed by a demodulator (Demod) 442 and an RX dataprocessor 444 to recover the rate sent by base station 450 for theterminal. A controller 420 receives the rate and provides coding andmodulation controls to TX data processor 412. Processor 412 generatesdata symbols based on the coding and modulation controls from controller420.

Controllers 420 x, 420 y, and 470 direct the operations of variousprocessing units at terminals 410 x and 410 y and base station 450,respectively. These controllers may also perform various functions forrate control. For example, controller 470 may implement process 200and/or 300 shown in FIGS. 2 and 3. Memory units 422 x, 422 y, and 472store data and program codes for controllers 420 x, 420 y, and 470,respectively. A scheduler 480 schedules terminals for data transmissionto/from base station 450.

The rate selection techniques described herein may be used for variouscommunication systems. For example, these techniques may be used for acode division multiple access (CDMA) system, a frequency divisionmultiple access (FDMA) system, a time division multiple access (TDMA)system, an orthogonal frequency division multiple access (OFDMA) system,an interleaved frequency division multiple access (IFDMA) system, aspatial division multiple access (SDMA) system, a quasi-orthogonalmultiple-access system, and so on. An OFDMA system utilizes orthogonalfrequency division multiplexing (OFDM), which partitions the overallsystem bandwidth into multiple (K) orthogonal frequency subbands. Thesesubbands are also called tones, subcarriers, bins, and so on. Eachsubband is associated with a respective subcarrier that may be modulatedwith data.

The rate selection techniques described herein may be implemented byvarious means. For example, these techniques may be implemented inhardware, software, or a combination thereof. For a hardwareimplementation, the processing units used to perform rate selectionand/or receiver spatial processing at a base station (e.g., RX spatialprocessor 460 and controller 470) may be implemented within one or moreapplication specific integrated circuits (ASICs), digital signalprocessors (DSPs), digital signal processing devices (DSPDs),programmable logic devices (PLDs), field programmable gate arrays(FPGAs), processors, controllers, micro-controllers, microprocessors,electronic devices, other electronic units designed to perform thefunctions described herein, or a combination thereof. The processingunits at a terminal may also be implemented with one or more ASICs,DSPs, processors, electronic devices, and so on.

For a software implementation, the techniques may be implemented withmodules (e.g., procedures, functions, and so on) that perform thefunctions described herein. The software codes may be stored in a memoryunit (e.g., memory unit 472 in FIG. 4) and executed by a processor(e.g., controller 470). The memory unit may be implemented within theprocessor or external to the processor.

The previous description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentdisclosure. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the disclosure. Thus, the present disclosure is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

What is claimed is:
 1. An apparatus comprising: means for receiving: arate selected for the apparatus based on a hypothesizedsignal-to-noise-and-interference ratio (SINR) for the apparatus, andcharacterized statistics of noise and interference observed at areceiver for the apparatus; and means for processing data in accordancewith the rate selected for the apparatus.
 2. The apparatus of claim 1,wherein said means for processing includes means for generating a pilotused to determine the hypothesized SINR for the apparatus.
 3. Theapparatus of claim 1, further comprising: means for determining achannel response estimate and a received SINR estimate for theapparatus; and means for computing the hypothesized SINR based on thechannel response estimate and the received SINR estimate.
 4. Theapparatus of claim 1, further comprising means for computing a capacityfor the transmitter based on the hypothesized SINR, the probabilitydensity function of the SINR loss, and an unconstrained capacityfunction.
 5. The apparatus of claim 1, further comprising means forcomputing a capacity for the transmitter based on the hypothesized SINR,the probability density function of the SINR loss, and a constrainedcapacity function.
 6. The apparatus of claim 1, further comprising meansfor computing a capacity for the transmitter based on the hypothesizedSINR, the probability density function of the SINR loss, the capacityfunction, and a back-off factor.
 7. A method, comprising: receiving arate selected for the apparatus based on a hypothesizedsignal-to-noise-and-interference ratio (SINR) for the apparatus, andcharacterized statistics of noise and interference observed at areceiver for the apparatus; and processing data in accordance with therate selected for the apparatus.
 8. The method of claim 7, wherein saidprocessing data includes generating a pilot used to determine thehypothesized SINR.
 9. The method of claim 7, further comprising:determining a channel response estimate and a received SINR estimate forthe apparatus; and computing the hypothesized SINR based on the channelresponse estimate and the received SINR estimate.
 10. The method ofclaim 7, further comprising computing a capacity for the transmitterbased on the hypothesized SINR, the probability density function of theSINR loss, and an unconstrained capacity function.
 11. The method ofclaim 7, further comprising computing a capacity for the transmitterbased on the hypothesized SINR, the probability density function of theSINR loss, and a constrained capacity function.
 12. The method of claim7, further comprising computing a capacity for the transmitter based onthe hypothesized SINR, the probability density function of the SINRloss, the capacity function, and a back-off factor.
 13. A computerreadable medium including instructions for execution on a controller,comprising: instructions to receive a rate selected for the apparatusbased on a hypothesized signal-to-noise-and-interference ratio (SINR)for the apparatus, and characterized statistics of noise andinterference observed at a receiver for the apparatus; and instructionsto process data in accordance with the rate selected for the apparatus.14. The computer readable medium of claim 13, wherein said instructionsto process data include instructions to generate a pilot used todetermine the hypothesized SINR.
 15. The computer readable medium ofclaim 13, further comprising: instructions to determine a channelresponse estimate and a received SINR estimate for the apparatus; andinstructions to compute the hypothesized SINR based on the channelresponse estimate and the received SINR estimate.
 16. The computerreadable medium of claim 13, further comprising instructions to computea capacity for the transmitter based on the hypothesized SINR, theprobability density function of the SINR loss, and an unconstrainedcapacity function.
 17. The computer readable medium of claim 13, furthercomprising instructions to compute a capacity for the transmitter basedon the hypothesized SINR, the probability density function of the SINRloss, and a constrained capacity function.
 18. The computer readablemedium of claim 13, further comprising instructions to compute acapacity for the transmitter based on the hypothesized SINR, theprobability density function of the SINR loss, the capacity function,and a back-off factor.